Real Time control Systems
Two of the more intuitive real-time systems that you can build in a general category called continuous media systems are:
1) Machine vision guided robotics (where an embedded or overhead camera is used to position a manipulator rather than position encoders and inverse kinematics - or use both) - I have found that this is great for teaching Rate Monotonic theory with hands on.
2) Digital audio decoding, transport over a network and encoding using a simple off-the-shelf sound card (VoIP or internet radio applications).
In the case of #1, you can see the effects of real-time response and computations used in guiding a robotic arm.
In the case of #2, you can hear any imperfections in real-time processing and transport with your ears.
Both are simple to build in a modest lab environment or in your home. To be accurate, you need to run off of interrupts and have microsecond or less latency on your hardware/software interface, so consider FreeRTOS and use of a simple camera port (ideally not USB since it has quite a bit of timing variation - or run low resolution on USB).